Sects, witches, and wizards-from Pythagoreans to Kepler

Mathematicians and their Gods

Over the next few weeks, Snezana Lawrence, co-author of Mathematicians and their Gods, introduced us into a Summer journey around the beauty of mathematics, trying to answer the question: will we ever need maths after school? In this second post, Snezana discusses popular perceptions of mathematics, from Pythagorean sect to the various interpretations of the supposed numerical values and hidden messages in the Bible.

As the summer is safely on its way (certainly in Sicily, where I write this on a terrace of one of its grand hotels) I think of the topics to discuss with friends and acquaintances over a glass of Prosecco when the rest of the party joins me in a week. To start a conversation based on mathematics may seem to some to be one of the tasks inevitably converging towards the plot-line of Mission Impossible. Well, certainly there are more pressing things that would occupy people’s minds, concerning international politics, the future of Europe, and the future of the Middle East. What’s new? These topics have occupied people’s minds for centuries. And inevitably there will be calls (as the amount of Prosecco increases) to discuss plots, pinpoint to patterns, make assumptions.

But there is unfortunately, in this particular sense, a similarity also with some popular perceptions of mathematics. From the Pythagorean sect, via various interpretations of the supposed numerical values and hidden messages in the Bible and other major religions’ sacred texts, to the phenomenon of ‘sacred geometry’ and the patterns upon which cities and institutions are built – mathematics history too has some questions that may be of interest in exploring the similar type of sentiment.

One response that answers all those questions wouldn’t satisfy anyone. So what examples can one come up with? Without going into much detail, one can mention that mathematicians, too, have been at times wrong, not completely, but a bit. Like for example Johannes Kepler whose mathematical model of the universe was, for a want of a better word, perfected over a period of time. One of his most surprising inventions came about when he taught mathematics at a school in Graz in his early career. He pondered: what if the five Platonic solids, are indeed some kind of blueprint upon which the universe is made as Plato suggested centuries earlier?

Plato, who discussed these solids in Timaeus (c. 360BC) associated them with four classical elements – Earth was represented by cube, air by octahedron, water by icosahedron, and fire with tetrahedron. The fifth element (yes just like the Fifth Element, the film by the French director Luc Besson, made in 1997) Plato thought, the dodecahedron, must have been used for arranging the constellations of the heavens. Furthermore, in the history of mathematics and philosophy, it was often identified as the element denoting divine spark, the principle of attraction, and the force that made all other elements come to life.

Forward to 1595 when Kepler worked on Platonic solids and used them to make a model of the universe, in his now famous book Mysterium cosmographicum (1596), illustrating the work with one of the most famous images of the history of science and mathematics. The image shows each Platonic solid encased in a sphere, inscribed in a further solid, encased in a sphere, which Kepler identified with the then six known planets: Mercury, Venus, Earth, Mars, Jupiter, and Saturn. Kepler described that the spheres containing the solids are placed at intervals corresponding to the sizes of each planet’s paths (as they were then known), assuming that they circled around the Sun.

Of course, later, whilst he was living in Prague, Kepler found that the orbital paths of planets of the Solar System were not circular but elliptical, but this beautiful model, even though not perfectly accurate, gave him an impetus for further research.

Kepler’s work on planetary motions and modeling the Solar System were based on his deep religiosity and theological convictions, connecting the spiritual and the physical ideas and imagery in his work. Kepler’s less known work is his Somnium, a novel about an imaginary journey that depicts his flight around the Solar System, guided by his mother. This novel was posthumously published, and not surprisingly, as his own mother Katharina Kepler, was accused of witchcraft in 1617. She was imprisoned and released in 1621, thanks partly to Kepler’s own efforts and involvement in the trial.

So what is one to make with this information? Was Kepler’s mother a witch, and was he a wizard of a kind? Is that how he worked out his laws of planetary motion? Of course our common sense takes over at this point. However, it is worth pointing out that it is much easier to do so with some time between us and Kepler in between, and during which the witches and wizards have safely made a transition from reality into fiction.

So, to get back to Sicily, my grand hotel’s balcony and Prosecco reception. And revisit the potential mathematical conversation, compare it with possible scheming and plotting that can be projected from the example of mathematics, from the secrecy of the Pythagorean sect, to the occult knowledge of Kepler, or the numerology of Newton to what is currently happening in Europe, the Middle East and generally in the world… Safe bet would be to get to know the details, actually know the real maths, and make cautious calculations. History of mathematics teaches us that models are prone to improvements over a period of time, just like Kepler’s model of the universe.

Snezana Lawrence is a Senior Lecturer in Mathematics Education at Bath Spa University. She has been involved with a number of national and international initiatives to promote the use of the history of mathematics in mathematics education. Snezana is on the Advisory Board of the History and Pedagogy of Mathematics Group (an affiliate of the International Commission on Mathematics Instruction), and is Mathematics Programme Director of the Prince's Teaching Institute Schools' Programme. She in on the Editorial Boards of BSHM Bulletin (as Associate Editor from January 2013) and Mathematics Today. Her website mathsisgoodforyou.com has attracted more than 4 million visitors since its launch in 2005. She is co-author of Mathematicians and their Gods.

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